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Accuracy question

• To: mathgroup at smc.vnet.net
• Subject: [mg14030] Accuracy question
• From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
• Date: Wed, 16 Sep 1998 14:12:09 -0400
• Sender: owner-wri-mathgroup at wolfram.com

In the lines below SetPrecision[Round,False] makes it so Precision and
accuracy return the actual floating point numbers that are used
internally. $NumberMarks=True, makes it so (among other things)
InputForm[num] returns all digits used internally, and the precision
marks at the end of inexact numbers.

In[1]:=
SetPrecision[Round,False];
$NumberMarks=True;
x=12345.67;
 
Out[2] shows exactly how Precision[x] is represented internally.  Out[3]
shows that Precision[x] is the number closest to  Log[10, 2^53].
 
In[2]:=
Precision[x]//InputForm

Out[2]=
15.9545897701910028`
 

In[3]:=
N[N[Log[10,2^53],17]]//InputForm

Out[3]=
15.9545897701910028`

The next line shows exactly how Accuracy[x] is represented internally.
Where does this number come from?
Since accuracy is the number of digits to the right of the decimal I
expect to get roughly 11.9.  But why 
( 11.8630751061039617` )?
 
In[4]:=
Accuracy[x]//InputForm

Out[4]=
11.8630751061039617`

______________________________
Cheers,
Ted Ersek